Differentiability of a Piecewise Function

Rarely Tested

Differentiability of a Piecewise Function

For a piecewise function at $$x=a$$, differentiability requires:

$$f'_-(a)=f'_+(a)$$

along with continuity at $$a$$.

Usage

- Used to determine unknown constants in piecewise functions and check differentiability at joining points.

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